Guo-Kuan Shao

Characterization of Sobolev regularity of plurisubharmonic functions

Let $f$ be a nonzero holomorphic germ at $0 \in \mathbb C^n$ with $f(0)=0$, and let $\chi$ be a $C^2$ non-decreasing convex function on the left half-line. We establish sharp necessary and sufficient conditions for the local Sobolev regularity of the plurisubharmonic function $v=\chi(\log|f|).$ The criteria for the $L^...